The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space

Shanzhen Lu; Dachun Yang

Studia Mathematica (1992)

  • Volume: 101, Issue: 3, page 285-298
  • ISSN: 0039-3223

Abstract

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We give a Littlewood-Paley function characterization of a new Hardy space HK₂ and its φ-transform characterizations in M. Frazier & B. Jawerth's sense.

How to cite

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Lu, Shanzhen, and Yang, Dachun. "The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space." Studia Mathematica 101.3 (1992): 285-298. <http://eudml.org/doc/215906>.

@article{Lu1992,
abstract = {We give a Littlewood-Paley function characterization of a new Hardy space HK₂ and its φ-transform characterizations in M. Frazier & B. Jawerth's sense.},
author = {Lu, Shanzhen, Yang, Dachun},
journal = {Studia Mathematica},
keywords = {Herz space; Littlewood-Paley function; new Hardy space; - transform},
language = {eng},
number = {3},
pages = {285-298},
title = {The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space},
url = {http://eudml.org/doc/215906},
volume = {101},
year = {1992},
}

TY - JOUR
AU - Lu, Shanzhen
AU - Yang, Dachun
TI - The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space
JO - Studia Mathematica
PY - 1992
VL - 101
IS - 3
SP - 285
EP - 298
AB - We give a Littlewood-Paley function characterization of a new Hardy space HK₂ and its φ-transform characterizations in M. Frazier & B. Jawerth's sense.
LA - eng
KW - Herz space; Littlewood-Paley function; new Hardy space; - transform
UR - http://eudml.org/doc/215906
ER -

References

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  1. [1] Y. Z. Chen and K. S. Lau, On some new classes of Hardy spaces, J. Funct. Anal. 84 (1989), 255-278. Zbl0677.30030
  2. [2] C. Fefferman and E. M. Stein, H p spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078
  3. [3] M. Frazier and B. Jawerth, The φ-transform and applications to distribution spaces, in: Function Spaces and Applications, Lecture Notes in Math. 1302, Springer, 1988, 223-246. Zbl0648.46038
  4. [4] M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170. 
  5. [5] J. García-Cuerva, Hardy spaces and Beurling algebras, J. London Math. Soc. (2) 39 (1989), 499-513. 
  6. [6] C. Herz, Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transform, J. Math. Mech. 18 (1968), 283-324. 
  7. [7] D. S. Kurtz, Littlewood-Paley operators on BMO, Proc. Amer. Math. Soc. 99 (1987), 657-666. 
  8. [8] S. Lu and D. Yang, Some new Hardy spaces associated with the Herz spaces, to appear. Zbl0782.42019
  9. [9] A. Torchinsky, Real-variable Methods in Harmonic Analysis, Academic Press, New York 1986. 
  10. [10] D. Yang, The boundedness of generalized Littlewood-Paley functions, Chinese Ann. Math. Ser. A 12 (1991), 736-744. Zbl0758.42013

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